A hane against an opponent's stone which forms a hane itself is called a counter-hane (hanekaeshi in Japanese).
Often a counter-hane will create a staircase shape.
See also Hanekaeshi followup.
Coconuts: Does this include the staircase and the cross cut only or am I missing something?
Bill: No, the crosscut is not a counter-hane. It is a counter to the hane, though.